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## NCERT Solutions for Class 11 Maths Chapter 11

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### Class 11 Maths Chapter 11 Conic Sections Solutions

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#### Important Terms on Conic Sections

- Circle, ellipse, parabola and hyperbola are curves which are obtained by intersection of a plane and cone in different positions
*Circle*: It is the set of all points in a plane that are equidistant from a fixed point in that plane.*Parabola*: It is the set of all points in a plane which are equidistant from a fixed point (focus) and a fixed line in the plane. Fixed point does not lie on the line.*Latus Rectum*: A chord through focus perpendicular to axis of parabola is called its latus rectum.

*Ellipse*: It is the set of points in a plane the sum of whose distances from two fixed points in the plane is a constant and is always greater than the distances between the fixed points.*Hyperbola*: It is the set of all points in a plane, the differences of whose distance from two fixed points in the plane is a constant.

##### Important Extra Questions with Answers on Conic Sections

- Find the centre and radius of the circle x² + y² – 6x + 4y – 12 = 0. [Answer: (3, -2), 5]
- Find the equation of hyperbola satisfying given conditions foci (5, 0) and transverse axis is of length 8. [Answer: x²/16 – y²/9 = 1.]
- Find the coordinates of points on parabola y² = 8x whose focal distance is 4. [Answer: (2, 4), (2, -4)]
- If one end of a diameter of the circle x² + y² – 4x – 6y + 11 = 0 is (3, 4), then find the coordinates of the other end of diameter. [Answer: (1, 2)]
- Find equation of an ellipse having vertices (0, 5) and foci (0, 4). [Answer: x²/9 + y²/25 = 1]
- Find the equation of a circle whose centre is at (4, –2) and 3x – 4y+ 5 = 0 is tangent to circle. [Answer: x² + y² – 8x + 4y – 5 = 0]
- If the distance between the foci of a hyperbola is 16 and its eccentricity is 2, then obtain the equation of a hyperbola. [Answer: x² – y² = 32]
- If the latus rectum of an ellipse is equal to half of minor axis, then find its eccentricity. [Answer: e = √3/2]
- Find the length of major and minor axis of the following ellipse, 16x² + 25y² = 400. [Answer: 10, 8]
- Find equation of circle concentric with circle 4x² + 4y² – 12x – 16y – 21 = 0 and of half its area. [Answer: 2x² + 2y² – 6x + 8y + 1 = 0]
- Find the equation for the ellipse that satisfies the given condition Major axis on the x-axis and passes through the points (4, 3) and (6, 2). [Answer: x²/52 + y²/13 = 1]